Introduction

Abstract

This chapter outlines the book’s objectives, and reveals that the reader will cover six branches of mathematics associated with rotation transforms: trigonometry, complex numbers, vectors, matrices, quaternions and multivectors. Complex numbers are extremely useful from two perspectives: the first is that they pave the way to the idea of a rotational operator, and second, they play an intrinsic part in quaternions and multivectors. Vectors provide a mechanism for representing directed lines, and together with complex numbers form the basis for quaternions, which provide a mechanism for rotating a point about an arbitrary axis. Lastly, multivectors introduce the concept of oriented areas and volumes, and provide an algebra for undertaking a wide range of geometric operations, especially rotations.